Kober was born in Billings, Montana on December 18, 1953. He moved to the Los Angeles area in his twenties and studied acting with the late thespian educator Ed Kaye-Martin. He is a student of Candace Silvers.

Kober is twice divorced. He married Rhonda Talbot on 4 February 1989; they had one child. On 25 August 1998, Kober married his second wife, fashion publicist Kelly Cutrone, founder of People’s Revolution, a fashion PR company. Their marriage ended in divorce. On 31 December 2013, Kober married his current wife, Adele Slaughter.

Kober may be best known as Dodger in China Beach and Daedalus in the short-lived cult horror series Kindred: The Embraced. He has made guest appearances on such television series as Buffy the Vampire Slayer, Law & Order: Special Victims Unit, CSI: Crime Scene Investigation, ER, 24, The Closer, New Girl, Criminal Minds, Star Trek: Voyager, and Star Trek: Enterprise. He played the character Julian Bradley in the two-part 1985 episode entitled “The Monster: Part 1&2” on Highway to Heaven. He played Jacob Hale, Jr. in the FX series Sons of Anarchy and Joe in the AMC series The Walking Dead. He also featured as DJ Ray from Reef Radio in Bacardi Rum’s 1990s ‘serve Chilled’ advertising campaign. In 2013, Kober reprised his role as Daedalus for the Kindred: The Embraced DVD set in a special features segment called “Daedalus: The Last Will and Testament,” which is meant for Abel (the boy Daedalus wanted to embrace in the episode “Romeo and Juliet”), who is now an adult and was embraced by Julian Luna as Kindred. He also played a role in 2005 film Love’s Long Journey.